NEW BOOK COMING SOON:

CHAPTER 1: ASSUMPTIONS

“In physics, certain ideas seem to have become so familiar to us that many have stopped thinking about how they are still, at their heart of hearts, indeed just assumptions. Commonly accepted frames of reference, useful for communicating relevant and necessary descriptions of the universe we live in for sure, but far from the tantalizingly simple theory of everything my intuition, the little idea whispering itself into my ear, told me must be there. The world at large assured me "space" and "time"..."exist". We, or at least I, was taught this from as far back as I can remember. With the exception of a short lived family imposed weekly church visit that didn't leave a remotely satisfying or believable creation story taste in my myth-I mean-mouth, I generally accepted, what I understood to be, the underlying solid bedrock of math, science and truth: Things exist in space, events occur in time, gravity is curvature of spacetime around mass, etc. That seemed simple enough for most. It really is simple once you understand the math. It's cohesive. The word "elegant" is often used to describe the equations and axioms that describe our universe. It works so well, in fact, I can confirm most, if not all, of the text book physics I was first introduced to, is almost completely built on those ideas as fundamental facts. But what eventually became clear to me, is that it is likely far more correct to say that while physics can, and does, accurately describe how spacetime behaves, it still comes up short when we ask it why or how spacetime exists or comes to be at all.

I would go on to read anything and everything i could by anyone who mentioned anything i thought remotely related to these idea. I became quite a weird little science nerd. I would try to work out what i believed in my head by visually walking through everything I knew to date, my model of my universe. I would end up at conclusions that demanded more and more explanation. In rare discussions, usually with teachers, i would argumentatively state that spacetime does not seem, itself, to be anything more than a construct, assumed and supposed into existence. I would get mad at the whole thing. Suppose spacetime exists. Suppose it has a geometry...some metric...then derive how that geometry curves (Einstein’s equations).

I would get annoyed groans and dismissive answers from both teachers and classmates when in class i dared pose questions along the lines of,

14 Year old Star Trek nerd Cody:

"Why don’t we derive spacetime, or explain its origin? Why don’t we ask if it could emerge from someth-"

Math Teacher (also my Phys-ed teacher):

"-From what Mr.Vaillant! This is Math not Philosophy or religious studies. Stop asking stupid questions"

Eventually, somehow, perhaps in a spiteful direct reaction to being told it was stupid to even wonder about such things, I became interested in what happens if we don’t accept that as a sufficient starting point. look I don't want to throw the baby out with the bath water here... Though my teenage self sure behaved as if he wanted to. I think I've been quite clear, even in just these opening lines, that the current framework of GR is not incorrect. I think it is a sufficient and useful scale dependent system that has amazing utility and value. I believe the 16 year old C student I was at the time may have verbally articulated those nuanced sentiments by declaring math useless and making said opinion known by routinely skipping class to play Area-51, a quarter hungry arcade game at Fat Cats Bar&grill, a pool hall near my high school. No, while dont advocate for a replacement of GR, I will however put forward some ideas here that may or may not convince you that this very system might simply be incomplete as far as a description of our universe goes.

The traditionalists tend to describe phenomena out there in our universe as if spacetime is the container or stage, in and on which matter and energy are the contents acting out their roles. Any grad student worth their weight in salt will be quick to interject that the division between matter and energy is, at best, arbitrary. So why oh why is the structure always described starting the same way? because for most cases it works ...Define spacetime, define what exists inside it then write down how those things move or interact. The pattern repeats everywhere. Newtonian mechanics presupposes absolute space and time. Special relativity presupposes spacetime with a constant speed of light. General relativity presupposes a dynamical spacetime that curves. Different theories, same kind of assumptions. Spacetime is always the foundation we assume.

When something is assumed to that degree at every level, it can risk becoming invisible. It becomes a blind spot. Something we forget to consider but even more accurately something we are trained to ignore. We treat it as given and move on. In scientific terms, these ideas want to be what are often be called "primitives", elements of a theory that are defined within but not necessarily derived from the framework in question. Primitives are necessary in the construction of a theory and are accepted as such as long as they are indeed minimal, necessary, and non-arbitrary. That is to say they not are derived from or decomposable into more fundamental components. Those most fundamental of parts are the primitives.

Spacetime, as one might assume, violates all three of those prerequisites. It is not minimal (The mathematical description of spacetime requires a manifold, metric tensor, coordinate system, curvature, and transformation rules). It is not necessary (Several formalisms exist that do not require spacetime to be assumed (these appear later)). And it is not non-arbitrary (There are many possible geometries; we simply choose one that agrees with our observation, point to it and say “This one is reality”).

Once I found my conceptual footing a bit here, something once out in the cognitive mist of almost understanding started to come into focus. If spacetime is assumed instead of derived then spacetime may not actually be a fundamental primitive. A theory that starts with spacetime can never explain spacetime. You can describe how it bends, how it stretches, how matter interacts with it, but you cannot explain why it is there. We don't accept that leap of logic anywhere else so readily as we do here.

Imagine explaining biology like this and being satisfied with the base assumption that life simply exists and the only scientific goal worth pursuing with regards to it is to strictly study what said life does now that it is here. While that is a valid field and pursuit in and of its self, it is not all encompassing of the wonders and mystery that understanding its origin would provide. We would call that level of inquiry on its own insufficient. We expect biology to try and explain how life originated, evolved and functions. Physics should hold itself to that same standard. For if you follow the former to its absolute limits it brings you to the doorstep of the latter and perhaps I can convince you as we move through these chapters that such a boundary exists down around the depths that Planck once probed with regards to spacetime...but I am getting ahead of myself again. More on that later as well.

Eventually I noticed another problem. If spacetime is fundamental, then everything must be explained in terms of it. But reality keeps presenting cases where spacetime just breaks down, plain doesn't work or becomes undefined. Black holes are the most famous example of this.

At the center of a black hole, our standard equations predict a singularity; a point where curvature becomes infinite and spacetime ceases to make sense. While most physicists don’t actually believe in a literal infinitesimal point type singularity (some do), it is more or less viewed as a not so subtle hint that the model you are using has reached a place it cannot describe. And that's a massive problem when it is supposed to describe everything. We don’t understand the core of a black hole because our description is built on spacetime, and black holes are environments where spacetime fails to adequately describe an event within itself.

Other examples of this are the many varied hypothesis for the beginning and end of the universe. We again predict seemingly indescribable events. A singularity, infinite density, zero volume, undefined geometry. Both the earliest moment, and the deepest most distant point of eventual gravitational collapse lead to a breakdown of spacetime as we understand it.

If spacetime were fundamental, you would expect it to hold under the most extreme conditions. Instead, those are the conditions where it fails spectacularly. Physics is not supposed to have “undefined” regions. When your most basic object (spacetime) fails at the boundaries of reality, that suggests spacetime is not the most basic object. When the medium breaks, the model built on that medium does not feel as fundamental.

Every spacetime collapse leaves the same unanswered question behind. What is more fundamental than spacetime?

I have stopped treating this question as something I can just continue to ignore. It eats at me when I lay awake at night and in every moment of quiet reflection. If a theory cannot describe its own boundary conditions, it needs to be revised or replaced. We need a framework that could describe black holes without singularities, the early universe without infinities & gravity without just assuming spacetime. If a foundational assumption repeatedly fails to describe what it claims to be a description of, I would argue that the scientific method begs and demands us to reassess its status as valid & irreducible framework primitive. Again, it's not "wrong", but definitely not the complete story.

Black holes and the Big Bang are not the only cases where this kind of persistent annoying wrinkle occurs. These are simply the low hanging fruit, the extremes of reality that seem to glaringly highlight the most likely areas where we would observe a theory breaking if indeed it was insufficient to describe such things. In Einstein’s equations spacetime is smooth until you push it to the limit. At a certain point the smoothness quickly becomes infinite curvature, infinite density & undefined space. Mathematically, this shows up as a classic division by zero problem. Conceptually, it shows up as a realization we may be pushing the wrong variable.

Trying to quantize gravity or trying to force spacetime into the language of particles has failed for almost 50 years. String theory, Loop quantum gravity, Causal sets, Spin foam, Twistors, Holographic duality. All different approaches. All elegant in their own way. Can you guess what they all have in common? They all start with spacetime or geometry and attempt to build upward. Even the “background independent” models assume a structure that behaves as if spacetime can be described discreetly. The assumption is omnipresent yet almost meticulously obscured in every case.

I reached a point where I had to write down the question plainly as an exercise in practical necessity. I bought a notebook. In it I wrote the line, "What if spacetime is not the right starting point?" A wistful philosophical exercise? Perhaps... But it helped me realize I didn’t just want a theory that adjusts spacetime. I wanted a theory that doesn’t require spacetime at all. Only when we can account for the emergence of it can spacetime be explained instead of assumed.

Once I allowed myself to question spacetime, I began looking at physics differently. Instead of treating it as the foundation, I treated it as a consequence that might emerge from something deeper. That distinction changes the very questions one asks. “How does matter move through spacetime?” becomes “What produces the appearance of spacetime in the first place?” Instead of wondering “How does gravity curve spacetime?” the question becomes “Why does curvature appear as gravity at all?”. When you flip the direction of explanation, you stop interpreting spacetime as a background and start treating it as a behavior.

To borrow a common analogy: If you study a flock of birds, you might, as I've done here, describe the collective as a single shape (a flock) moving across the sky. But the flock is not a fundamental object in our reality. It’s a pattern that emerges from individual birds following simple rules. The pattern is real, useful at this particular scale and meaningfully observable to us but it is not a fundamental primitive. It clearly is made up of smaller units (the birds). Now this is not a perfect example because, well, the same logic can be applied to seemingly infinite levels of sub differentiation. The birds are to the flock as the birds organs are to its body, the cells to the tissues that make up the organs, this is mirrored in the many nested systems, organisms, organelles, structures, chemicals, hormones and various signaling patterns that subsequently make up the untold branches of every science that is or will be.

Is it so outlandish to think Spacetime may be similar? A pattern, a behavior, a way of describing relationships and not a thing simply imbued with existence of its own that we are to accept at face value? What even are the underlying elements that would generate the pattern we've come to call spacetime?

Whatever this thing is, it seems by definition it must exist before geometry, exist without reference to distance, and operate without needing spacetime. It must encode structure that becomes geometry through some transition. I hadn’t named that “something” yet but it was more tangible and definable now than before. I had a more confident feeling now that spacetime was possibly not the bottom layer. That realization removed a barrier I didn’t know existed in my mind. Suddenly I was left sitting with the uneasy but exciting idea that if spacetime itself isn't fundamental, then reality doesn’t have to be built out of things located in space and time. It opens up a very different line of thinking. It allowed me to play with the idea that perhaps the universe is not just a container with objects inside it following the laws we observe but perhaps all we observe is emergent from even more robust fundamental relationships. And i wondered if this incomplete picture might explain the failures (edge cases) where GR just does not cut it.

Once you allow yourself to think of reality as relationships instead of objects, another observation becomes clear: Physics rarely measures “things”. It instead tends to measure "differences". We don’t measure an absolute location, an absolute time, or an intrinsic property that exists on its own. We measure how one thing relates to another. The distance between two points, the duration between two events, the energy difference between two states. Even in quantum mechanics (where this frustration with GR eventually led me), what we call a “state” is not a thing. It’s a set of probabilities describing relationships among possible outcomes. This may sound like a subtle difference, but the implications are quite large. If physics only ever measures relationships then relationships may be more fundamental than the objects they relate. In other words Spacetime seems to only encode relationships: “Here” vs. “there”, “Now” vs. “then”, “Before” vs. “after”. Physics doesn’t measure spacetime directly. It measures the correlations between events. That means spacetime could be more a model of relationships and not necessarily the cause of them.

To try and elaborate on this idea and why it is so intriguing to me in more clarity let’s consider a simple example. We might say something like, “These two points or particles are 1 meter apart.” But what does that actually mean and what are we really describing? Is it how long it takes for light to travel between them? That's not horrible intuition at all and there are many useful cases where this works just fine but is it a full description? I kept feeling like I was trying to gather smoke with a butterfly net or herd feral cats. As I tried to wrap this up in a nice neat bow it quickly became clear that each definition I drafted only led me to the realization that it was itself insufficient and I needed to move the goalpost, so to speak, again and again. It became necessary to include more and more I had not initially considered. Every conversation had, paper or book read, lecture listened to, only served to force me to expand the already messy, blurry, smeared perimeter around the dark mysterious shape of what so desperately needs to be given form and definition. Perhaps you might, like much of the reference material, think it sufficient, as I once did, to simply say that a statement like this describes how they (the point/particles) influence one another in spacetime or other relevant field. Or maybe how their relationship to one another at time of measurement (usually but not always the now) can be used to define the full spectrum of possibilities available to said points in said system...Given that we are of course privy to the rules that govern it. I've come to view it as more of a range, spectrum or landscape of more or less likely states available for the components to occupy or navigate. So what do you think? Can the potential interactions, implied in this simple statement of distance measurement (“These two points or particles are 1 meter apart.”), themselves not also be seen to encode similarly probabilistic (yet more abstract) relationships of concepts (akin to "likeness", "separateness etc.) on to yet another plane of ever increasingly complex dimensional variables?

Did I lose you? No?

Ok, so let's take stock of where we are. Distance is not a substance. It is a label we assign to the strength or degree of relationship between at least two measurably distinct and separate potential states. We transition this from a philosophical position to more of an observation when one considers that in general relativity, distance can literally change depending on energy and motion. If spacetime were fundamental, distance should be fixed. Instead, distance is ultimately flexible and variable. Variables are not often found in foundations but appear naturally as consequences of deeper rules. So if spacetime is a description of relationships, what determines the relationships? Physics itself seems to taunt us and hint at a deeper layer where relationships can be said to come first, leading to spacetime as a convenient way to describe them.

The deeper I looked, the more one pattern repeated. Every time physics made progress, it did so by removing something we once assumed was fundamental.

Earth is not the center of the universe.

Matter is not continuous; it is quantized.

Time is not absolute.

Space is not fixed.

Each breakthrough removed a layer of assumption. Yet somehow, spacetime itself had remained relatively untouched. We kept modifying it (curvature, expansion, topology) but we rarely dared step outside of it. On the occasion someone did they could never quite fend off the inevitable monsters in the data or manage to knit it all together neatly enough to sway the rest of us. This, to me, feels like it may be just the next in a long line of assumptions to fall? The moment was i able to entertain that idea seriously, other observations began to click into place. Quantum mechanics does not require spacetime to define a state. It defines a system using a vector (a state) in an abstract space. Quantum field theory places "fields" on "spacetime", but the fields themselves can, at least in some special limited edition flavours of advanced algebraic QFT, be defined before or independent of geometry...So what's going on there? And information theory, a domain where we analyze structure without reference to physical location, is entirely, you guessed it, spacetime-independent.

Classical mechanics deals with Particles in space. Relativity tackles the Geometry of spacetime. Quantum mechanics steps in where States and relationships are concerned. Information based theories take it even further and try to reduce everything to distinctions logic and structure. Two of those do not need spacetime at all. Quantum mechanics and information theory talk about states,

correlations, and distinctions ... none of which require the background of spacetime as I had come to understand it.

That raised even more unsettling possibilities to mentally explore. I wondered If quantum mechanics and information theory work without spacetime, and general relativity breaks where spacetime collapses, then spacetime may, as I have long suspected, simply be the most effective description of our reality and not the fundamental fabric of it. From this perspective, I hope we can collectively agree to shift the question from “What is spacetime?” to “What produces spacetime?”.

To move forward, I needed a different starting point...and If we don’t begin with spacetime, what do we begin with?

Suddenly I am 14 again and I hear "Derive it from what Mr. Vaillant?" The booming voice of authority wakes a long dormant part of my psyche I thought dead and gone. "This is math class, not philosophy or religious studies" So let's stick to the math then.

Physics offers a clue, though it rarely acknowledges it directly. The most fundamental mathematical object used in modern theory is not space, or time, or geometry. It is the "state". In quantum mechanics, everything begins with the state of a system. A state isn’t a location. It isn’t a particle. It isn’t a point in space. It’s a mathematical object encoding all possible outcomes and the relationships between them. We can represent a state without assigning it a position or a moment in time. A state is simply a complete description of what can be known. That makes states more general than spacetime. Spacetime can only describe where and when things are. A state on the other hand can describe a rich variety of correlations, constraints, relationships, probabilities, structure. None of these require a background geometry at all. In fact, geometry can be defined from them. This led me to the realization that if a state contains all the information necessary to define relationships, then spacetime could be one possible representation of those relationships.

Not the only representation mind you, just the one we experience internally. Like a user interface, it is what we interact with most readily. Not the data itself, but a useful visualization of it that allows us to manipulate and navigate it naturally. A subtle shift again but one worth noting. I went from “What is spacetime made of?” to a more general “What structure would make spacetime appear?” That question turned out to be far more productive perhaps exactly because it doesn’t just, as we have been doing with the old tools, immediately assume the answer.

Once the idea of "state first, spacetime second" gelled long enough without being rejected by my mind, the next obvious step was to examine what a “state” really means. No, I am not invoking some Jordan Peterson-esque straw man, tail chasing adage here, though I'd forgive you for feeling this is equally as frustrating. As even I am aware of how pedantic this line of inquiry can feel on first read. But humor me here, I promise I won't tell you to clean your room or quote the bible dressed as a Batman villain. Consider this. In everyday language, a "state" can sounds vague, ethereal, fuzzy even. Emotion is a state. Weather is a state. In physics it much more cleare, a state is a very specific thing with a clear definition. A "state" in this sense is the minimum information required to fully describe a system at an instant. Again, I will point out it is not a location nor a moment in time. A state is the information itself.

In classical mechanics, the state of a particle is described by its position & its momentum. In quantum mechanics, we replace that with something much more general and use a vector in a high-dimensional space that encodes all possible outcomes. The important difference is that in quantum theory, position is part of the description of the state. The state does not explicitly require position to exist. Remember, a state does not need spacetime. It is Spacetime that needs a state. Spacetime tells you where things are.

The state tells you what things are and how they can relate. Spacetime is a coordinate system laid on top of the state, not the generator of the state.

To understand the implications of this, consider another simple thought experiment: If two particles are entangled, they share correlations independent of distance. If you move one across the room—or across the galaxy— the correlations stay exactly the same. Nothing about the entangled state changes. The correlations don’t weaken with distance because the correlations don't care about or depend on distance. Through this lens entanglement doesn’t seem to live in spacetime at all. It feels more intuitive to say it resides in some other informational structure. This line of thought led me to seriously consider that distance is, at least in a few specific ways, less fundamental (by comparison) than correlation is.

Spacetime can stretch, warp and compress. Relative distances can and do change. This is why something like interferometry works. Even the generally accepted rate of expansion of the universe can be seen, in some situations, to appear to indicate an increase in separation between celestial bodies in such ways that we are regularly left with confusing observations of objects seeming (to us) to be racing away from us (accelerating even) faster than our current frameworks can explain away, without invoking numerous and cumbersome ad hoc additions of exotic things like "dark energy" (not to be mistaken for "dark matter" which is that other unseen something that can be observed influencing the rotation of galaxies and the like) in an attempt to try and duct tape theories together...Yet correlations between quantum states remain constant in this shifting sea... until something finally interacts with or, in other words, measures them. Correlations persist even when spacetime does not.

Once I started thinking in terms of states and correlations instead of objects in space, it became easier to see that spacetime behaves a lot like an interface. And an interface should not be confused with the system itself. Nor a map for the terrain, as I've come to learn. It is what the system shows to the user, how the user interfaces with reality. Not entirely unlike how a phone displays apps or files as icons. They look like independent objects and have utility from the perspective of the user but behind the screen, beneath the pixels that make them up they are structured information, stored as electrical states. The interface and its icons exist for the user’s benefit, not because the system fundamentally stores information as pictures but because it is the most efficient representation of information for a particular use at this particular level and scale of meaningful interaction. Just as the GUI is a representation of a more complex underlying operational software on a computer or device so the analogy can be extended to include other similarly useful comparisons. In this analogy the everyday aspects of experience can be viewed in this way too. Space and time, as we've touched on, can be said to interface with the representation layer of physics. When dealing with matter and fields it's more useful to treat them as the "icons" & "files" that are representative of physics' higher-level constructs. Quantum states, in my opinion, are the best candidate if you are trying to get at the underlying data in, or fundamental description of a system.

When you drag two icons next to each other on a computer, they only appear to get closer. Nothing underneath the interface becomes closer or farther apart as far as the system is concerned. The spatial representation is a convenience for the user. A simplification of commands and conditions. A compressed representation. Likewise is the case when we say two particles are a meter apart. We are describing a relationship between complex objects and rules from inside our interface, not the underlying structure. The actual physics, if i am not mistaken here, happens at the level of correlations in the states. The “distance” is how we visualize that specific relationship, not what creates it. This perspective seems to highlight a major common confusion. If we assume the universe needs spacetime to function (because we almost exclusively experience reality through it) then we should accept that the interface, or our perception of it, is mainly shaped around the limitations of our own mammalian perception, and may not fully reflect the nature of the underlying system at all. The universe may not “think” in space and time but we sure do. Humans have a hard time picturing much more than three dimensions of space and one of time. Should that be so surprising considering we are a product of such a space. Perhaps we see what we see because we are so used to looking at things with a narrow human observational bias, limiting as it may be, to make sense of relationships, to navigate physical experience and to reason about cause and effect. Spacetime could be said to represent the visualization layer of reality. An artifact of some process, but just a few paragraphs in and already its seeming less and less likely you'd be so quick to call it the architecture itself. So if spacetime is the interface, what is the system underneath?

Information.

When I say “information,” I don’t really mean like data on a hard drive or like numbers written in a notebook or anything like that. I mean something much more basic. Information, in the most general sense, needed a new definition. I tentatively landed on the following though who knows if this will be anywhere close to the final wording i will land on in the end. Information, by my definition, is a distinction that makes a difference. If two states are identical in every way, then there is no information between them. If they differ in any way (position, spin, energy, charge, correlation) that difference is information. A system with many possible distinct states has high information capacity and a system that has few or only one possible state, has none. Here, Information is defined without reference to space or time. You don’t necessarily need a location or a ticking clock to define a difference or express a relationship. Information exists whether or not spacetime exists. This makes information a candidate as a deeper foundational building block. It satisfies the very criteria spacetime falls apart under. It is Independent of geometry yet can define structure through patterns. It apparently survives black holes, can exists outside of or independent of time and can generate relationships without the need for our precious fundamental fabric of spacetime. Black holes obliterate spacetime geometry, but they show evidence that they likely preserve information on the boundary. Quantum entanglement persists regardless of distance because correlations are defined independent of geometry. Information doesn’t care where or when things are. Information simply is. From this perspective, space and time are mere methods of organizing information but not the origin of it. If we follow this further we can, if not now maybe by the end of this book, agree that we no longer need to try and explain the universe by just compulsively filling "space" with "stuff" and "things" over "time". We need to explain how "information" organizes itself such that "spacetime" pops out as the simplest representation of it. Spacetime, in this context, becomes a resultant format, not a foundational substance; It's Not what exists in space and time, but rather, I'd push to say, it is how things can and do relate in more of a space of possibility or potential, and how each iterative moment (quantized information state) to the next, could actually generates the experience of space emerging over these sequential states, stacking to become the persistent arrow by which we measure time.

I hope I have not lost anyone yet or bored you to death talking in circles with this introductory first chapter. It only gets harder from here so lets recap before we launch into the actual bulk of the theory. Everything up to this point was clearing space in your head to prime you for this perspective shift. As it stands, Spacetime is assumed, the assumption is unjustified, physics works fine without it at the fundamental level and information remains meaningful where spacetime fails.

Once you can entertain that as readily as you once presupposed spacetime, the next steps will seem straightforward enough.

Let's build a model that starts with information, and show how spacetime appears from it.

Simple right?

I will try to keep the chapters focused and short to allow you to pause and consider the ideas as we move through them.”

C.L.Vaillant